Suck Creek Cycles is pretty good. Check them out at http://www.suckcreek.com/ They are on Cherokee Blvd. River City Bikes isn't very good. Their customer service is horrible. Perhaps they have changed, but I have waited a half hour before being helped. If interested though, check them out at http://www.rivercitybikes.com/
There is also Owen Cyclery and East Ridge, but I don't know anything about them.
I am partial to Owen Cyclery. I bought my first new bike there in 1994. At the time, old Mr. Owen was still alive. His son took over; now I think another guy is running the place. I forget his name, but he was about to marry when I ran across him on a ride in Knoxville in 2003. He is a really nice guy, and presumably that would translate into a good person to do business with.
Google and you will find the address. It is on the main drag in Hixson.